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Proof step 17 from proof embed-split (previous step)

((P0 * P1))(mk(rs, f)), ∀ r. r ∈ rs → g(r) = a, ∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ P0[rs0, f] ∧ P1[rs1, f] ⊦ ((a[P0] * a[P1]))(mk(rs, f, g))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0[rs1, f], P1[rs0, f], ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1 ∪ rs0, f, g))

Proof step 17 from proof embed-split (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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